The present invention is directed to a real time measurement system for a moving web using a Kalman filter algorithm and, more specifically, to measurements on a web which are based on a mechanical scanning sensors traversing across the moving web.
In feedback control processes for moving webs and especially in the paper-making industry, a scanning sensor traverses the web and measures a parameter such as basis weight, moisture, caliper or coating. Also, the same is true in other industries such as metal rolling and the manufacture of fabric, rubber and flooring materials. As will be described in conjunction with the preferred embodiment, when a scanner is scanning across a moving sheet the sampling or measurement intervals (databox values) are not equal due to both the back-and-forth scanning movement and the so-called offsheet turn-around time. But for good feedback control, it is desired to provide continuous estimates of the entire perpendicular profile under the scanner each time one of many so-called databox measurements is made. Thus, it is desired to generate a cross direction profile estimate as if they were generated from a non-scanning device.
What is desired is optimal state estimation of the profile. It is known that a Kalman filter in conjunction with the Gauss-Markov process equations theoretically can do this. But differential matrix equations including exponential matrices must be solved and when these may involve matrices of 240xc3x97240 once every 20 milliseconds, computational complexity makes standard use of the Kalman filter impossible. And this is especially true of a scanning process where, for example in a paper-making process where the paper sheet moving several feet per second, means that any effective feedback control must be quickly accomplished.
The Kalman filter algorithm is well-known in estimation theory as fully described in the McGraw-Hill Encyclopedia of Science and Technology, Vol. VI, 7th Edition, pp 483-486.
It is a general object of the present invention to provide an improved real time measurement process for a moving web.
In accordance with the above object, there is provided a real time measurement process for a moving web where a scanning sensor traverses the web and a measured parameter is fed back via a computer on-line to control an actuator which can change the parameter and where measurement or sampling intervals are not equal, and where the scanning sensor has a plurality of databox measurement positions as it scans across the web, the process comprising the following steps of using the Kalman filter algorithm to predict and update values of said parameter to provide continuous values for said feedback control including using the Gauss-Markov equation
y(t)=H(t)xc3x97(t)+u
where y(t) is the observed parameter value, H is a matrix which is dependent on databox position of the scanner and which changes with each different databox measurement and u is a scalar representing the noise associated with each measurement, and where the H matrix is solved by the computer not as a matrix but as a vector to significantly reduce computational complexity.